Klein Bottle

Non-orientable surface with no inside — impossible in 3D without self-intersection

Rotation speed: 1.0

Resolution: 40

Style:

u slice: full

Klein bottle: a closed non-orientable surface. χ = 0, H₁ = ℤ ⊕ ℤ/2ℤ. Immersion in ℝ³ requires self-intersection.

Boundary word: aba⁻¹b (square identification). Cannot be embedded in ℝ³. In ℝ⁴: no self-intersection.